erm I think it is actually possible, technically, with Dish, however not legal so cannot be discussed here.
In any case, you realistically have 2 options - 1) control your STB and 2) digitise the output.
Control allows you to maintain full quality by keeping the signals going direct to your TV/Amp, yet control the STB/TV/Amp through LMCE, so that when you choose live TV, it will switch the TV/AMP inputs to your STB, and control the channel/volume up/down through the LMCE interfaces (remote, web pad, mobile phone, etc) leaving you with an apparently fully integrated system with single control interface
Digitise allows you to bring the video and audio streams into LMCE so that it can redistribute them to any MD around your house, record them, etc.
Control will only allow you to view Sat on in the one entertainment area, ie not redistribute the media around the house to other MDs
Digitise will likely loose some of your quality as you are typically converting from digital to analogue back to digital again.
Only capturing with a DVB-S card will allow you to realise both Pros and avoid both Cons.